This may have been a problem I saw in some math book, whose details I don’t remember.
A cow is tied to a rope which is attached to a silo. The silo has a diameter of 1 unit. The rope is pi/2 units long. What is the exact area the cow can roam?
I haven’t figured this out. I’ve tried polar coordinates, parametric equations, etc. This is probably going to turn out like part 2 of the circles problem…
This is almost a year old, and I’m surprised I haven’t uploaded it here yet. Enjoy :)
My first Nivvix entry turned out a lot more dramatic than I would have liked, so I decided to do another one. This one is a Nivvixian mathematician, loosely based on a species of praying mantis. He lives a calm, quiet life in the countryside, and is developing the set of rules and principles that may someday form the core of Nivvixian math.
Nivvix doctor, based on a june bug. It’s one of the first search results I got for “medicinal insect”.
He was driven to a little bit of fanaticism by modern medicine and colleagues who made fun of him. He jumps on each of their failures, and makes sure all his patients know that the traditional, alchemic medicines and good ol’ stone cot can never be replaced, and that they’ve made the right choice coming to him. Not everyone’s convinced.
Okay, so I’ve moved art back to here because four sites is just too many to check.
Many numbers can be expressed as the sum of two palindromes. 389 for instance is 383 + 6 as well as 323 + 66.
What three-digit number cannot be expressed as the sum of two palindromes?
(For the sake of this problem, palindromes with leading zeroes [like 030 and 0550] are not allowed, and neither are negative numbers or non-integers. Single digits are allowed.)
I’ve been playing Spore lately, and came across a curious problem. Here it is in story form.
“Hello Omnipotent! You look fabulous as always…” After hearing it basically word-for-word a thousand times, the compliment wore thin.
“Yes, thank you. I’ve come to discuss diplomatic matters,” said the Suna pilot.
The Green Empire’s representative’s tinny voice continued. “Anything! Name it.”
“Well, as you know, we’ve been in conflict with the Notcute for some time now. It’s usually no trouble chipping away at their dozens of T0 planets. But there’s a particular planet which we’ve lost three spaceships to. Not by any virtue of their defenses, of course. For some reason, all the ship’s computers cease function when we near it. Thyragnis, it’s called.”
“Very curious! What would like us to do?”
“We’d like you to attack that planet, and capture it. And keep it. We don’t want it.”
“We’re big fans of disorder! We’ll do it. We need 52000 dollars.”
But Omnipotent had 99999999 dollars on board that he preferred to bask in a little while longer. “How about I just give you this one purple spice and call it good?”
“Done!” Suckers, thought the Green Empire.
Green was oblivious to the Suna’s obvious goal to take possession of the entire galaxy, or at least one arm of it. The two Empires were about the only ones left in the local bubble. The next day, a Suna ship arrived as close to Thyragnis as possible and launched their communicator.
“Hello Omnipotent! You look fabulous as always…”
“Yes yes, I was wondering if you’d like to set up a trade route.”
“Would we ever!”
And in no time, the Suna bought the planet for a nice price of 3000000.
Then they promptly began to clean the Green empire off the map. The Green Empire still happily considered them allies, even after they bombed their fourth planet. But then after the humor wore off they retaliated.
“Omnipotent!” yelled another Suna on board. “They’re attacking!”
“It’s just pirates again. It’s always pirates. You know, why don’t they just say, ‘It’s pirates – don’t worry about it’? And don’t get me started on those blasted ecodisasters.”
“No, this one’s not pirates. I swear. It’s the Green.”
“Well, by the time they take one of our planets, we’ll have taken five of theirs.”
“They’re about to take Thyragnis.”
And they did. Even though the Suna now owned every other system, The Green empire had a tight hold on Thyragnis, and the Suna could do nothing about it. Their onboard computers scrambled on each attempt to approach the planet.
“Crocodilus, I’d like you to attack someone for me…”
This planet did indeed crash the game every time. Buying Thyragnis solved the problem, and they didn’t really make an attempt to get it back, but I thought it would have been a real cunning trick on the part of the developers if they did.
It’s the birth of the modern nalvot world. A war has just ended and Raspaka is the hotbed of civilization.
Oli, a warmswimmer from a small shoreside farming town, heads to Raspaka to get an education. But he’s in for much more, including sports, art, journalism, love, and a newfound spirituality. Follow him as he makes friends, spars with professors, and experiences life in the city.
This was my third attempt at Nanowrimo, and it was pretty different this time around. I got over 100,000 words, and I tried something I thought was downright impossible – to incorporate Christianity (or an allegory of it) into a completely alien setting. I didn’t do illustrations this time, but I did come up with some sketches at HexFactorial. Over there’s some excerpts too. It was fun speaking in an ‘uneducated’ voice. I’m glad I did it in first person, but now I’ve started talking like Oli. XD Third person next year.
This problem’s probably shown up before by a different name or different variation, but I thought it was interesting. It goes like this.
I have a block of wood with integer dimensions. If I saw off two units from each dimension, the volume of the woodblock reduces by half. How many possible sets of dimensions are there for the original block? Or, what integers satisfy 2xyz = (x+2)(y+2)(z+2)?
You can see a program generate them here. There’s eighteen but I could have sworn there were twenty, when I made a similar program some years ago.
The problem changes when you vary the proportion and the number of units cut off from each dimension. (If the proportion is p, 1/p is the how much of the volume is left after cutoff.)
When c=1 and as p increases, there are less and less solutions. 2,3,4 (1,2,3) is the only solution when c=1 and p=4. No solutions when c=1 and p>=5.
When p=2 and as c increases, there are more and more and larger solutions.
It appears that the trend when p=c and both increase is that there are less solutions, though since they become large, and because waiting for it to process is a pain for high maximum values, I’m not sure about this one. With max of 1000 and p=c=11, it didn’t find any solutions.
Let me know if you find anything interesting. :)
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